The methods of finding stability regions of uncertain linear systems

In this thesis, Hurwitz and Schur stability problems of uncertain linear systems are considered. The fixed inertia regions for one and two parameters polynomials are determined. The problem of n × n polynomial matrix family, in both Hurwitz stability and Schur stability, is considered. It is shown that in the robust Hurwitz and robust Schur stability the problem can be reduced to positivity of the specially constructed multivariable polynomials. Outer approximation to the set of Hurwitz and Schur stability monic polynomials is considered in polynomial space. The reflection coefficients for Hurwitz and Schur stability are obtained and using these coefficients the existence of stabization parameters for continuous or discrete linear systems are investigated. Results are illustrated by an adequate number of examples.